The NFL schedule came out a few days ago and it was a bit disappointing for me. In all but the last two weeks there are Thursday night games (well, the season opener is on a Wednesday if you want to be pedantic), which makes a road trip much easier to plan than it was before. Whereas in past years it would take a few hours to come up with a viable route, this year it took about 30 minutes. The following road trip might not be optimal, and naturally I'm not taking it as I'm moving to Singapore in August, but for what it's worth, here is a trip that takes you to all 32 stadiums (yes the Giants and Jets play at the same place but the experience is different).
Sep 5 Dallas at NY Giants Sep 9 Buffalo at NY Jets Sep 10 Cincinnati at Baltimore Sep 13 Chicago at Green Bay Sep 17 Denver at Atlanta Sep 20 NY Giants at Carolina Sep 23 NY Jets at Miami Sep 30 Tennessee at Houston Oct 1 Chicago at Dallas Oct 4 Arizona at St. Louis Oct 7 Baltimore at Kansas City Oct 14 New England at Arizona Oct 15 Denver at San Diego Oct 18 Seattle at San Francisco Oct 21 Jacksonville at Oakland Oct 25 Tampa Bay at Minnesota Oct 28 Carolina at Chicago Nov 4 Chicago at Tennessee Nov 5 Philadelphia at New Orleans Nov 8 Indianapolis at Jacksonville Nov 11 San Diego at Tampa Bay Nov 15 Miami at Buffalo Nov 18 Baltimore at Pittsburgh Nov 22 Houston at Detroit Nov 25 Buffalo at Indianapolis Nov 26 Carolina at Philadelphia Dec 3 NY Giants at Washington Dec 9 Dallas at Cincinnati Dec 10 Houston at New England Dec 16 Washington at Cleveland Dec 23 Cleveland at Denver Dec 30 St. Louis at Seattle
You could flip those last two depending on where you wanted to spend Christmas and New Year's as Seattle hosts the 49ers on the 23rd and KC visits Denver on the 30th.
In the past, the typical trip requires about 28,000 miles of driving; this one is somewhat shorter at just 25,000, assuming Toronto as a start and end point. I'm also ignoring practical problems such as driving from Denver to Seattle in the winter, which might cause some difficulties. Some of the drives are quite long, with about 20 days having a journey of greater than 500 miles so it's not something that I'd want to do alone. It would not surprise me if someone did a trip this year though as the additional midweek games make it pretty easy.